Many elite colleges and universities make a real effort to recruit (some) students from low income backgrounds who went to relatively poor high schools. New data shows that's not enough to remedy the damage that bad high schools do.

State universities recruiting more disadvantaged students? Great! But common sense—along with this new study from the NBER—tells you that you can't fix the problems in our education system by targeting kids after they've already had 12 years of inadequate public education. The study found that the quality of a student's high school is "a key predictor" of their grades in college, meaning that without a serious dose of remedial studies, kids from disadvantaged high schools are doomed to be at a disadvantage themselves in good colleges full of kids who attended better high schools. From Inside Higher Ed:

Over all, measures of high school quality explain 20 percent of the
variation in high school grades, and that variation is not substantially
reduced in the years that follow, the report says. (Measures of high
schools include both socioeconomic statistics such as percentage of
students from low-income backgrounds, which historically correlates with
limited resources at high schools, and the percentage of students
taking college admissions or Advanced Placement tests.)

The findings showed that for kids who came from similar socioeconomic backgrounds, the quality of their high school is what predicted how they did in college.

From this we may draw the reasonable conclusion: If you want to fix higher education for disadvantaged students, first fix their high schools. And before that fix their middle schools and elementary schools. And before that, get that Universal Pre-K going.